Kepler unbound: some elegant curiosities of classical mechanics

Niall J. MacKay, Sam Salour

Research output: Contribution to journalArticlepeer-review


We explain two exotic systems of classical mechanics: the McIntosh-Cisneros-Zwanziger (“MICZ”) Kepler system, of motion of a charged particle in the presence of a modified dyon; and Gibbons and Manton's description of the slow motion of well-separated solitonic (“BPS”) monopoles using Taub-NUT space. Each system is characterized by the conservation of a Laplace-Runge-Lenz vector, and we use elementary vector techniques to show that each obeys a subtly different variation on Kepler's three laws for the Newton-Coulomb two-body problem, including a new modified Kepler third law for BPS monopoles.
Original languageEnglish
Pages (from-to)47-52
Number of pages6
JournalAmerican Journal of Physics
Issue number1
Publication statusPublished - Jan 2015

Cite this